normed vector space in a sentence

Examples

1. An important theorem about continuous linear functionals on normed vector spaces is the Hahn Banach theorem.
2. Its vectors form an inner product space ( in fact a Hilbert space ), and a normed vector space.
3. When speaking of normed vector spaces, we augment the notion of dual space to take the norm into account.
4. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space.
5. :Usually, normed vector space are meant to be vector spaces over the field of real or complex numbers.
6. Consequently, for normed vector space ( and hence Banach spaces ) the Bourbaki Alaoglu theorem is equivalent to the Banach Alaoglu theorem.
7. In the case of a normed vector space, the polar of a neighbourhood is closed and norm-bounded in the dual space.
8. An inner product space is a normed vector space, and the inner product of a vector with itself is real and positive-definite.
9. As this property is very useful in functional analysis, generalizations of normed vector spaces with this property are studied under the name locally convex spaces.
10. In mathematical analysis, the "'Minkowski inequality "'establishes that the L " p " spaces are normed vector spaces.